FractAlphic Frolix

A fractal is a shape that contains smaller (and smaller) versions of itself, like this:

The hourglass fractal


Fractals also occur in nature. For example, part of a tree looks like the tree as whole. Part of a cloud or a lung looks like the cloud or lung as a whole. So trees, clouds and lungs are fractals. The letters of an alphabet don’t usually look like that, but I decided to create a fractal alphabet — or fractalphabet — that does.

The fractalphabet starts with this minimal standard Roman alphabet in upper case, where each letter is created by filling selected squares in a 3×3 grid:


The above is stage 1 of the fractalphabet, when it isn’t actually a fractal alphabet at all. But if each filled square of the letter “A”, say, is replaced by the letter itself, the “A” turns into a fractal, like this:








Fractal A (animated)


Here’s the whole alphabet being turned into fractals:

Full fractalphabet (black-and-white)


Full fractalphabet (color)


Full fractalphabet (b&w animated)


Full fractalphabet (color animated)


Now take a full word like “THE”:



You can turn each letter into a fractal using smaller copies of itself:







Fractal THE (b&w animated)


Fractal THE (color animated)


But you can also create a fractal from “THE” by compressing the “H” into the “T”, then the “E” into the “H”, like this:




Compressed THE (animated)



The compressed “THE” has a unique appearance and is both a letter and a word. Now try a complete sentence, “THE CAT BIT THE RAT”. This is the sentence in stage 1 of the fractalphabet:



And stage 2:



And further stages:





Fractal CAT (b&w animated)


Fractal CAT (color animated)


But, as we saw with “THE” above, that’s not the only fractal you can create from “THE CAT BIT THE RAT”. Here’s what I call a 2-compression of the sentence, where every second letter has been compressed into the letter that precedes it:


THE CAT BIT THE RAT (2-comp color)


THE CAT BIT THE RAT (2-comp b&w)


And here’s a 3-compression of the sentence, where every third letter has been compressed into every second letter, and every second-and-third letter has been compressed into the preceding letter:

THE CAT BIT THE RAT (3-comp color)


THE CAT BIT THE RAT (3-comp b&w)


As you can see above, each word of the original sentence is now a unique single letter of the fractalphabet. Theoretically, there’s no limit to the compression: you could fit every word of a book in the standard Roman alphabet into a single letter of the fractalphabet. Or you could fit an entire book into a single letter of the fractalphabet (with additional symbols for punctuation, which I haven’t bothered with here).

To see what the fractalphabeting of a longer text in the standard Roman alphabet might look like, take the first verse of a poem by A.E. Housman:

On Wenlock Edge the wood’s in trouble;
His forest fleece the Wrekin heaves;
The gale it plies the saplings double,
And thick on Severn snow the leaves. (“Poem XXXI” of A Shropshire Lad, 1896)

The first line looks like this in stage 1 of the fractalphabet:


Here’s stage 2 of the standard fractalphabet, where each letter is divided into smaller copies of itself:


And here’s stage 3 of the standard fractalphabet:


Now examine a colour version of the first line in stage 1 of the fractalphabet:


As with “THE” above, let’s try compressing each second letter into the letter that precedes it:


And here’s a 3-comp of the first line:


Finally, here’s the full first verse of Housman’s poem in 2-comp and 3-comp forms:

On Wenlock Edge the wood’s in trouble;
His forest fleece the Wrekin heaves;
The gale it plies the saplings double,
And thick on Severn snow the leaves. (“Poem XXXI of A Shropshire Lad, 1896)

“On Wenlock Edge” (2-comp)


“On Wenlock Edge” (3-comp)


Appendix

This is a possible lower-case version of the fractalphabet:

He Say, He Sigh, He Sow #49

• «Планета есть колыбель разума, но нельзя вечно жить в колыбели.» — Константин Эдуардович Циолковский (1911)

• “Planet is the cradle of mind, but one cannot live in the cradle forever.” — Konstantin Tsiolkovsky

Crowley on Crystals

The first thing to meet our eyes [on a Himalayan expedition in 1902] was what, suppose we had landed in the country of Brobdignag, only more, so, might have been the lace handkerchief of a Super-Glumdalclitch left out to dry. It was a glittering veil of brilliance of the hillside; but closer inspection, instead of destroying the illusion, made one exclaim with increased enthusiasm.

The curtain had been formed by crystalline deposits from a hot spring (38.3° centigrade). The incrustation is exquisitely white and exquisitely geometrical in every detail. The burden of the cynicism of my six and twenty years fell from me like a dream. I trod the shining slopes; they rustled under my feet rather as snow does in certain conditions. (The sound is strangely exhilarating.) It is a voluptuous flattery like the murmurous applause of a refined multitude, with the instinctive ecstatic reverence of a man conscious of his unworthiness entering paradise. At the top of the curtain is the basin from which it proceeds, the largest of several similar formations. It is some thirty-one feet in diameter, an almost perfect circle. The depth in the middle is little over two feet. It is a bath for Venus herself.

I had to summon my consciousness of godhead before venturing to invade it. The water steams delicately with sulphurous emanations, yet the odour is subtly delicious. Knowles, the doctor, and I spent more than an hour and a half reposing in its velvet warmth, in the intoxicating dry mountain air, caressed by the splendour of the sun. I experienced all the ecstasy of the pilgrim who has come to the end of his hardships. I felt as if I had been washed clean of all the fatigues of the journey. In point of fact, I had arrived, despite myself, at perfect physical condition. I had realized from the first that the proper preparation for a journey of this sort is to get as fat as possible before starting, and stay as fat as possible as long as possible. I was now in the condition in which Pfannl had been at Srinagar. I could have gone forty-eight hours without turning a hair. — The Confessions of Aleister Crowley: An Autohagiography (1929)

Dull ’Un

There was a lot of drinking. One sunny morning [Dylan] Thomas and friends were in a field above Newlyn, sampling a “champagne wine tonic” sold by a local herbalist. Thomas talked and talked, then stopped abruptly. “Someone’s boring me,” he said. “I think it’s me.”


After his Vassar reading, Thomas stayed with a staff member at the college, Vernon Venable. He and his hosts sat up half the night, talking and drinking. When he finally retired, Venable sat on the bed while Thomas launched into a drunken account of his unhappiness. According to Venable, it went on for hours — “just misery, misery, misery, which seemed to me so pervasive that it had no source except a psychological source. That is, the man was deeply neurotic.” Venable is unable to remember details, except that part of the monologue was concerned with his love for Caitlin [Thomas, his wife]. In effect, says Venable, he was declaring that life was a nightmare and he couldn’t stand it. […]

In the morning Venable said goodbye to his guest, then discovered to his annoyance that Thomas had stolen his best white shirt. — Dylan Thomas, Paul Ferris (1977) (ch. 7, “Caitlin”, and ch. 10, “Laugharne and America”)

The Psyve Mind Speaks

“H.P. Lovecraft were really underrated in terms of the sixties bands from the West Coast.” — Psychic Hi-Fi: Genesis Breyer P-Orridge’s Favourite Albums, The Quietus, 23i2014.


Previously pre-posted:

He Say, He Sigh, He Sow #23 — an earlier engagement by Genesis P. Orridge in terms of issues around “in terms of” (dot dot dot)
Ex-term-in-ate!

Sigh-Lent Night

Morrissey’s stag night, like sim. Descriptive of a public house peopled entirely by broken men of indeterminate age staring silently at their half-empty pint glasses. […]

mortal adj. Refreshed (qv) within an inch of one’s life.

mortal combat n. Fighting between intoxicated fellows. Or occasionally, in the case of certain self-sufficient Harold Ramps (qv), between a single intoxicated fellow. — from Roger’s Profanisaurus: Das Krapital, The Revolutionary Dictionary of Bad Language (Viz 2010)

Nice Von

“If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.” — John von Neumann

This quote is popular on web pages about von Neumann, and about computing and mathematics generally. It is apparently not from a published work of von Neumann’s, but Franz L. Alt recalls it as a remark made from the podium by von Neumann as keynote speaker at the first national meeting of the Association for Computing Machinery in 1947. The exchange at that meeting is described at the end of Alt’s brief article “Archaeology of computers: Reminiscences, 1945–1947”, Communications of the ACM, volume 15, issue 7, July 1972, special issue: Twenty-fifth anniversary of the Association for Computing Machinery, p. 694. Alt recalls that von Neumann “mentioned the ‘new programming method’ for ENIAC and explained that its seemingly small vocabulary was in fact ample: that future computers, then in the design stage, would get along on a dozen instruction types, and this was known to be adequate for expressing all of mathematics…. Von Neumann went on to say that one need not be surprised at this small number, since about 1,000 words were known to be adequate for most situations of real life, and mathematics was only a small part of life, and a very simple part at that. This caused some hilarity in the audience, which provoked von Neumann to say: ‘If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.’ ”

Source of John von Neumann quote

Colorfool

Album primo-avrilesque, meaning April-Foolish Album, is a collection of visual jokes published by the French humourist Alphonse Allais (1854-1905) on 1st April 1897. Note that some of the captions can’t be translated fully into English, because they use French idioms that refer to color.

Combat de nègres dans une cave, pendant la nuit
Negroes fighting in a cellar at night


Stupeur de jeunes recrues apercevant pour la première fois ton azur, O Méditerranée!
Astonishment of young naval recruits seeing for the first time your blue, O Mediterranean!


Des souteneurs, encore dans la force de l’âge et le ventre dans l’herbe, boivant de l’absinthe
Pimps, still in the prime of life and with bellies to the grass, drinking absinthe
(Pimps were then known as dos verts or “green-backs”)


Manipulation de l’ocre par des cocus ictériques
Handling of ochre by jaundiced cuckolds
(According to one page I’ve found, coucou is the name given to some yellow wild-flowers, and cuckolds can be yellow with jealousy)


Récolte de la tomate par des cardinaux apoplectiques au bord de la mer Rouge (Effet d’aurore boréale)
Harvesting of tomatoes by apoplectic cardinals on the shore of the Red Sea (effect of the Aurora Borealis)


Ronde de pochards dans le brouillard
Dance of drunks in the fog
(Slang for “drunk” in French is gris, which also means “gray”)


Première communion de jeunes filles chlorotiques par un temps de neige
First communion of anaemic young girls in snowy weather


Marche funèbre, composée pour les funérailles d’un grand homme sourd
Funeral March, composed for the obsequies of a great deaf man


Tolk of the Devil

I’ve said it before and I’ll say it again: I wish someone would translate Lord of the Rings (1954-5) into English. By that I mean (of course) that I wish someone would translate LOTR into good English. I’ve looked at Tolkien’s bad English in “Noise Annoys” and “Science and Sorcery”. Here’s another example:

Pippin declared that Frodo was looking twice the hobbit that he had been.

“Very odd,” said Frodo, tightening his belt, “considering that there is actually a good deal less of me. I hope the thinning process will not go on indefinitely, or I shall become a wraith.”

“Do not speak of such things!” said Strider quickly, and with surprising earnestness. – The Fellowship of the Ring (1954), Chapter 11, “A Knife in the Dark”

Strider should have added: “Or in such a way!” In the second paragraph, Frodo suddenly talks like a Guardian-reader. Why on earth did Tolkien use “thinning process”, “indefinitely” and “actually” amid otherwise good, simple English? Thinning is obviously a “process”, so there’s no need to say it is, and “indefinitely” and “actually” are badly out of a place in a fantasy novel, let alone in dialogue there. “Considering” is less bad, but it should go too. I would improve the paragraph like this:

“Very odd,” said Frodo, tightening his belt, “seeing that there is now a good deal less of me. I hope the thinning will not go on much longer, or I shall become a wraith.”

Now there’s nothing incongruous: the only un-English word is “very”, but that doesn’t seem un-English on the tongue or to the eye. The Guardianese is gone, but it should never have been there in the first place. Tolkien should not have written like that in Lord of the Rings. And not just as a professional scholar of language: simply as a literate Englishman. H.W. Fowler’s Modern English Usage (1926) had been in print for twenty-eight years when The Fellowship of the Ring was first published. It’s hard to believe that Tolkien wasn’t familiar with it.

If he wasn’t, that’s a great pity. If he was, the bad prose in LOTR becomes even more inexplicable and unforgiveable. Alas for what might have been! Imagine if, per impossibile, Tolkien’s masterwork had been edited by the second-greatest Catholic writer of the twentieth-century, namely, Evelyn Waugh.

When bad prose appears in something by Waugh, it’s deliberate:

I had a fine haul – eleven paintings and fifty odd drawings – and when eventually I exhibited them in London, the art critics, many of whom hitherto had been patronizing in tone as my success invited, acclaimed a new and richer note in my work.

Mr. Ryder [the most respected of them wrote] rises like a fresh young trout to the hypodermic injection of a new culture and discloses a powerful facet in the vista of his potentialities … By focusing the frankly traditional battery of his elegance and erudition on the maelstrom of barbarism, Mr. Ryder has at last found himself.Brideshead Revisited (1945), Book II, “A Twitch Upon the Thread”, ch. 1

Waugh was deliberately mocking the mixed-metaphor-strewn prose and pretensions of modern critics. Waugh paid great attention to language and compared writing to carpentry. It was a craft and good craftsmen do not work carelessly or use bad materials. Nothing in Brideshead is careless or casual, as we can see when the narrator, Charles Ryder, first meets the “devilish” æsthete Anthony Blanche, who has “studied Black Art at Cefalù” with Aleister Crowley and is “a byword of iniquity from Cherwell Edge to Somerville”. Blanche has a stutter and Waugh uses the stutter to underline his iniquity. Or so I would claim. Here is Blanche engaging in some papyrocentric performativity:

After luncheon he stood on the balcony with a megaphone which had appeared surprisingly among the bric-à-brac of Sebastian’s room, and in languishing, sobbing tones recited passages from The Waste Land to the sweatered and muffled throng that was on its way to the river.

“’I, Tiresias, have foresuffered all,’” he sobbed to them from the Venetian arches –
“Enacted on this same d-divan or b-bed,
I who have sat by Thebes below the wall
And walked among the l-l-lowest of the dead….”

And then, stepping lightly into the room, “How I have surprised them! All b-boatmen are Grace Darlings to me.” Brideshead Revisited, Book I, “Et in Arcadia Ego”, ch. 1

Talking about the Greek sage Tiresias, who experienced life as both a man and a woman, Anthony Blanche, a man whose surname is the feminine form of the French adjective blanc, meaning “white”, stumbles over the initial consonants of three words: “divan”, “bed” and “lowest”. Is it a coincidence that the same consonants, in the same order, appear in the Greek diabolos, meaning “devil”?

I don’t think so. If Blanche had stuttered on “surprised” too, I would be even more certain. But the –s isn’t essential. After all, it was lost as diabolos journeyed from Greek to Latin, from Latin to French, and from French to English, where it appears as “Devil”. And what does Charles Ryder later call Anthony Blanche after Blanche has spent an evening tête-à-tête trying to turn Ryder against Ryder’s great friend Sebastian Flyte? You can find out here, as Ryder discusses the evening with Sebastian:

“I just wanted to find out how much truth there was in what Anthony said last night.”

“I shouldn’t think a word. That’s his great charm.”

“You may think it charming. I think it’s devilish. Do you know he spent the whole of yesterday evening trying to turn me against you, and almost succeeded?”

“Did he? How silly. Aloysius wouldn’t approve of that at all, would you, you pompous old bear?” – Brideshead Revisited, Book I, “Et in Arcadia Ego”, ch. 2

Blanche is “devilish” and his reputation for “iniquity” is well-deserved. That’s why I think the three words over which Blanche stutters were carefully chosen by Waugh from The Waste Land. Waugh was a logophile and that is exactly the kind of linguistic game that logophiles like to play.